Photovoltaic cells produce a voltage that varies with current, cell operating condition, cell physics, cell defects, and cell illumination. One mathematical model for a photovoltaic cell, as illustrated in FIG. 1, models output current as:
                    I        =                              I            L                    -                                    I              0                        ⁢                          {                                                exp                  ⁡                                      [                                                                  q                        ⁡                                                  (                                                      V                            +                                                          I                              ⁢                                                                                                                          ⁢                                                              R                                S                                                                                                              )                                                                                            n                        ⁢                                                                                                  ⁢                        k                        ⁢                                                                                                  ⁢                        T                                                              ]                                                  -                1                            }                                -                                    V              +                              I                ⁢                                                                  ⁢                                  R                  S                                                                    R              SH                                                          EQN        .                                  ⁢        1            Where
IL=photogenerated current
RS=series resistance
RSH=shunt resistance
I0=reverse saturation current
n=diode ideality factor (1 for an ideal diode)
q=elementary charge
k=Boltzmann's constant
T=absolute temperature
I=output current at cell terminals
V=voltage at cell terminals
For silicon at 25° C., kT/q=0.0259 Volts.
Typical cell output voltages are low and depend on the band gap of the material used to manufacture the cell. Cell output voltages may be merely half a volt for silicon cells, far below the voltage needed to charge batteries or drive most other loads. Because of these low voltages, cells are typically connected together in series to form a module, or an array, having an output voltage much higher than that produced by a single cell. Additionally, two or more strings of multiple photovoltaic cells are sometimes electrically coupled in parallel to increase capacity.
Real-world photovoltaic cells often have one or more microscopic defects. These cell defects may cause mismatches of series resistance RS, shunt resistance RSH, and photogenerated current IL from cell to cell in a module. Further, cell illumination may vary from cell to cell in a system of photovoltaic cells, and may vary even from cell to cell in a module, for reasons including shadows cast by trees, bird droppings shadowing portions of a cell or module, dust, dirt, and other effects. These mismatches in illumination may vary from day to day and with time of day—a shadow may shift across a module during a day, and rain may wash away dust or dirt shadowing a cell.
From EQN. 1, output voltage is greatest at zero output current, and output voltage V falls off nonlinearly with increasing output current I. FIG. 2 illustrates the effect of increasing current drawn from a photovoltaic device at constant illumination. As current I is increased under constant illumination, voltage V falls off slowly, but as current I is increased to an output current near the photocurrent IL, output voltage V falls off sharply. Similarly, cell power, the product of current and voltage, increases as current I increases, until falling voltage V overcomes the effect of increasing current, whereupon further increases in current I drawn from the cell cause power P to decrease rapidly. For a given illumination, each cell, module, and array of cells and modules therefore has a maximum power point (MPP) representing the voltage and current combination at which output power from the device is maximized. The MPP of a cell, module, or array will change as temperature and illumination, and hence photo-generated current IL, changes. The MPP of a cell, module, or array may also be affected by factors such as shadowing and/or aging of the cell, module, or array.
Maximum Power Point Tracking (MPPT) controllers for operating a photovoltaic device at or near its maximum power point have been proposed. These controllers typically determine an MPP voltage and current for a photovoltaic device connected to their input, and adjust their effective impedance to maintain the photovoltaic device at the MPP.
Photovoltaic devices are typically subjected to one or more production line tests. For example, a photovoltaic device is often characterized using a “flash test,” where the device is exposed to light of known intensity, such as a “1 sun” (1,000 watts per square meter) light source, while sweeping a load across the device from open circuit to short circuit, or vice versa. Voltage and current data is recorded during the load sweep, and device open circuit voltage (Voc), short circuit current (Isc), and maximum power point (Pmp) are determined from the recorded data. These device characteristics are used, for instance, to ensure device quality and/or to bin devices according to Voc, Isc, and/or Pmp.
As another example, photovoltaic devices are often subject to “electroluminescence” (EL) testing at one or more times during device production. EL testing includes forcing a test current through the photovoltaic device in a direction opposite to that which current normally flows through the device, thereby causing the device to emit infrared light. The infrared light is imaged to detect device imperfections, such as device cracks, thereby helping ensure device quality.
A photovoltaic device may also be subject to reverse current, which is current flowing through the device in a direction opposite to that of normal operation. For example, consider a scenario where first and second strings of photovoltaic devices are electrically coupled in parallel, and each string includes multiple series-coupled photovoltaic devices. Forward current will flow through both strings if the strings have identical current-voltage characteristics, where a string's current-voltage characteristic depends on both its physical properties and its operating conditions. For example, consider a situation where the first string is exposed to strong sunlight and the second string is mostly shaded. This illumination difference will cause the first string to produce a larger photo-generated current than the second string, such that the strings have different current-voltage characteristics, potentially resulting in a reverse current flowing through the second string.